A checksum is a small-sized datum derived from a block of digital data for the purpose of error detection which may have been introduced during its transmission or computer storage. It is usually applied to an installation file after it is received from the download server. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authentication.
The actual algorithm which yields the checksum from a data input is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm will usually output a significantly different value, even for small changes made to the input. This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted.
Checksum functions are related to , fingerprints, randomization functions, and cryptographic hash functions. However, each of those concepts has different applications and therefore different design goals. For instance, a function returning the start of a string can provide a hash appropriate for some applications but will never be a suitable checksum. Checksums are used as cryptographic primitives in larger authentication algorithms. For cryptographic systems with these two specific design goals, see HMAC.
and are special cases of checksums, appropriate for small blocks of data (such as Social Security numbers, bank account numbers, computer words, single , etc.). Some error-correcting codes are based on special checksums which not only detect common errors but also allow the original data to be recovered in certain cases.
With this checksum, any transmission error which flips a single bit of the message, or an odd number of bits, will be detected as an incorrect checksum. However, an error which affects two bits will not be detected if those bits lie at the same position in two distinct words. Also swapping of two or more words will not be detected. If the affected bits are independently chosen at random, the probability of a two-bit error being undetected is 1/ n.
A single-bit transmission error then corresponds to a displacement from a valid corner (the correct message and checksum) to one of the m adjacent corners. An error which affects k bits moves the message to a corner which is k steps removed from its correct corner. The goal of a good checksum algorithm is to spread the valid corners as far from each other as possible, so as to increase the likelihood "typical" transmission errors will end up in an invalid corner.